Matlab symbolic variables depending on time "t" and call of symbolic vector elements

Hi everybody :)

I have the following problem :

syms t x(t) y(t) z(t) theta1(t) theta2(t)

Y = [0 cos(theta1);1 sin(theta2)] * [x y]'

now the first problem is that when I call the first element of the vector V with the command "V(1)" I does't become the first element of the vecotr V but rather the hole vector with 1 instead of t, I mean :

cos(theta1(1))*conj(y(1))

conj(x(1)) + conj(y(1))*sin(theta2(1))

but what I want is this :

cos(theta1(t))*conj(y(t))

I mean only the first element which depends on t that I defined at the first of the script .

now the second little problem is that I want to give to theta1 and the other symbolic variables a start value but when I write this :

theta1(0) = 5 I become an error :

Error using symfun>validateArgNames (line 165) Second input must be a scalar or vector of unique symbolic variables.

Error in symfun (line 42) y.vars = validateArgNames(inputs);

Error in sym/subsasgn (line 1640) C = symfun(B,[inds{:}]);

Error in test (line 9) theta1(0)=5

thx for helping me !! :)

Answer 1

[Mischa Kim]

Mohamed, to your first question: use instead

 Y = [0 cos(theta1);1 sin(theta2)] * [x; y]  % note the last semi-colon
 Y =
        cos(theta1(t))*y(t)
 x(t) + sin(theta2(t))*y(t)

At that point you can start substituting values. E.g.

 subs(Y,{theta1},{0})
 ans =
                       y(t)
 x(t) + sin(theta2(t))*y(t)

Does that help?

[Mohamed Amine Chaaleb]

Thx Kim for your answer but actually I don't want to substitute elements from the vector but rather call its elements.

[Mischa Kim]

Could you give an example of what exactly you want to do and what the result is supposed to look like?

[Mohamed Amine Chaaleb]

when I use a normal vector for example :

 B=[5;6]

calling the first element of the vector would look like : B(1) so I'll get the result 5 and my problem is that when I use the symbolic tool for example

syms t theta(t) x(t)

    A=[cos(theta) x]

using the command A(1) for calling the first element of the vector A like what I done by B will show the following result

    A=
        cos(theta(1)) 
        x(1)

But what I want is to get the first element :

 cos(theta(t))

so I can use it independently of the vector A ...so my question is how can I call the first element of a vector with symbolic elements that depends on time.

thx :)

[Mischa Kim]

OK. Yes you can, but it is a bit cumbersome. The challenge is that it is not possible to create an array of symfuns, as far as I am aware.

 Y  = [0 cos(theta1);1 sin(theta2)] * [x; y];
 Y  = Y(t);               % convert symfun to sym...

 Y1fun = symfun(Y(1),t);  % ...and convert back to symfun
 Y1fun(3)
 ans =
 y(3)*cos(theta1(3))

[Mohamed Amine Chaaleb]

thx :) !!! this is what I was looking for :)